Average Luminosity of Moving Body: A Relativistic Analysis

[Tahmeed]

Lets suppose a radiating body moving relative to a frame. At a certain time because of relativistic beaming one observer in that frame would observe a different luminousity of the body. But observes placed at a different angle in that frame relative to the body would also observe different lluminousity. What is the average luminousity if we average all the observed luminousity of observes placed at different angle in that frame?

 

[Ibix]

What do you think? There are a number of simple ways to deduce this.

Hint: What is the answer in the case of non-relativistic motion? What changes at high relative speeds?